The Islanders have completed the painful process of learning which players fit or don’t fit the program, which players are on board (and on the board) for Rebuild Year 2. Perhaps now is the time to re-up one greybeard playmaker for leadership, ability and continuity.

Doug Weight has resumed skating, with a goal of playing the final 7 or 8 games of this season. If it were completely his call, the games would not be his last in an Islanders uniform.

“Let’s put it this way: there’s nothing that’s making me run from Long Island,” Weight told us with a smile after practice on Wednesday. “I love it here and I love this organization and the guys on the team. There’s nothing I’d like more than to get something done for next season.”

“Something,” of course, is a one-year contract. Like the Islanders, Weight has the option of seeing what the July 1 opening of unrestricted free agency brings. But the first choice of the 38-year old center is to finalize a deal – the sooner the better.

“This is not a case of seeing if the grass is greener on July 1,” Weight said. “I know what we have here with the Islanders and I’m very excited about it. With a lot more health and whatever changes management makes, this team can go from the bottom of the league to the playoffs next season. I truly believe that.

“I can’t tell you how much I’d kill to be in the playoffs next season in an Islanders uniform. This place has come to mean a lot to me. They gave me a chance last summer to prove I had something left, and we proved it together. I’m going to play next season, and I hope it’s here.”

As does Weight protege Josh Bailey, who’s too young to openly campaign for a player’s return but is not hesitant to share how much the veteran’s tutelage has helped him. Ironically, we first cornered Bailey about this subject on game night on Feb. 28, about an hour before Bill Guerin took his Islanders uniform off for the last time. It was for a story we never wrote about the leadership of potential tradees Guerin, Weight and Brendan Witt.

“Dougie’s been amazing for me,” Bailey said then. “Every day I learn something from him. At practices, on the bench during games, he always has some positive input that will stay with me for my whole career.”

With Guerin, Mike Comrie and Chris Campoli gone, it would make sense for the Islanders to have Weight as a veteran leader at center while Brendan Witt and Mark Streit return on the blueline. Through the rocky moments in this challenging season, Weight has been respected by the press and heralded by management, coaching staff and most importantly his teammates for being a pro’s pro.

The depth chart at center next season minus Weight is Josh Bailey, Frans Nielsen, Nate Thompson and – a huge maybe – John Tavares or Matt Duchene. (Dean McAmmond is UFA). That blend of skill and (lack of) experience is swell if you’re Boston University. The Islanders need a veteran presence in the middle. They also need someone with poise on the bench and on the power play.

Could the Islanders find a veteran who’s closer to 30 than 40? Possibly, but you never know if a free agent is going to be a prize or a bad apple. The coaching staff already knows the player they have in Doug Weight. Better yet, the kids like Bailey and Nielsen already know the man they have in Doug Weight.